Tensile[89]

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Florida State University *

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3003

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Mechanical Engineering

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Dec 6, 2023

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1 LAB REPORT 2 Gabriel Parsonis Oct/10/2022 Objective The objective of this lab is to better understand how a tensile-tension test works and how it applies to engineering stress/ strain and true stress/strain. This lab provided the first opportunity for students (this semester) to have hands on experience working real engineering testing technology in a laboratory setting. Students after the lab should be able to visualize the differences of ductility and strength between two materials and how they can be measured or visually observed before and after testing. Experimental: Figure 1: Polycarbonate specimen before and after tensile testing

2 Figure 2: Aluminum specimen before and after tensile testing Figure 3: Data collected representing plastic and metal pre and post testing measurements

3 Figure 4: Aluminum specimen Excel Sheet1 Figure 5: Aluminum specimen Excel Sheet2

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4 Figure 6: Aluminum specimen Excel Sheet3

5 Figure 7: Plastic specimen Excel Sheet1 Figure 8: Plastic specimen Excel Sheet2

6 Results and Discussion: Part I. Experimental Results and Data Analysis of Al alloy Samples 1. With the raw data obtained from the tension test, compute and plot engineering stress s vs. engineering strain e. The plot should be generated with a computer (e.g., Microsoft Excel). No credit will be given to a hand-generated plot. To find the engineering stress vs strain graph, one must individually calculate the Engineering Strain (stroke/original length) and Engineering Stress (force/original area) for each of the three specimens (Figure 9). Following this an average of each point must be taken in order of there to be a singular line in a singular graph (Figure 10). Engineering Strain on the X axis and Engineering Stress on the Y axis. Figure 9: -50 0 50 100 150 200 250 300 350 -0.05 0 0.05 0.1 0.15 0.2 0.25 0.3 Engineering Stress Engineering Strain Similarity of Stress/Strain Curves for three Aluminum tests

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7 Figure 10: 2. Compute and plot true stress s vs. true strain e. Plot on the same graph as engineering stress vs. engineering strain so that you can clearly see the differences between the curves. Figure 11: The true stress/strain curve (yellow line) was derived from the average engineering stress/strain numbers. True stress was found by multiplying engineering stress with (1+engineering strain) and true strain was found by taking ln (1 + engineering strain). y = 22,904,741.73x 6 - 22,382,902.23x 5 + 6,991,959.97x 4 - 775,408.52x 3 - 7,029.65x 2 + 6,602.01x R² = 0.99 y = 5770x 0 50 100 150 200 250 300 350 0 0.05 0.1 0.15 0.2 0.25 Engineering Stress Engineering Strain Averages for stress vs strain for the three Aluminum Tests y = 22,904,741.73x 6 - 22,382,902.23x 5 + 6,991,959.97x 4 - 775,408.52x 3 - 7,029.65x 2 + 6,602.01x R² = 0.99 y = 5770x 0 50 100 150 200 250 300 350 400 450 0 0.05 0.1 0.15 0.2 0.25 Stress Strain Averages for stress vs strain for the three Aluminum Tests with true stress and strain curve

8 a) Elastic property and strength measures 1. Determine the elastic modulus E. To determine the Modulus, one first must find the average of the 3 graphs as one graph. Following this they then find the trendline of the “straight portion” of this graph leading to the yield point. Then the slope of this line is the Elastic modulus which is y=5770x. 2. Determine the 0.2% offset yield strength (sY) . In order to obtain the 0.2% offset. One must first calculate the 0.2% offset yield point. To determine this one must obtain the 0.2 percent offset stress and strain. The 0.2 strain is found by adding 0.2% in excel to the average of the three strains and the stress is found through multiplying the modulus and the avg strain. The plot for this on the graph demonstrates where the yield point is (grey line and blue line). Through finding the yield point if one locates its coordinates on the graph the which is 241 on the y axis. b) Ductility measures 1. Determine the true fracture strain. In order for one to find the true fracture strain they must divide the largest average strain by the original length. 0.23568 / 25 = 0.0094272

9 2. Determine the percent reduction in area. Before test: 5.76 mm (width) 1.59 mm (thickness) 9.1584 mm^2 (area) After test: 5.53 mm (width 1) 1.53 mm (thickness 1) 5.49 mm (width 2) 1.50 mm (thickness 2) 5.51 (avg width) 1.515 (avg thickness) 8.34765 (avg area) Calculations: = [(Old-new)/old] *100 = [(9.1584-8.34765)/ 9.1584] *100 = 8.85 percent 3. Determine the toughness of the material. In order to find the toughness of a curve one must find the area under the curve through integration. Here the best formula one could derive is ( 22,904,741.73x6 - 22,382,902.23x5 + 6,991,959.97x4 - 775,408.52x3 - 7,029.65x2 + 6,602.01x ). Once deriving this equation, one must then integrate from 0 to 0.229337773 (largest strain number) so the integral takes the entire curves length into account entire curve length. However, I was unable to find a website that worked into deriving a proper number. 4. Does this material exhibit necking? Yes, this material exhibits necking. One could tell visually from the in-elastic, shape deformation the material goes through. In addition to this the material necks after the UTS is hit as the slope of the graphs becomes negative.

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10 c) Determine the power-hardening constants (K, n) in the equation s = K(e^n). Use only the data before the onset of necking. (Note that the power-hardening relationship is an approximation of a true stress vs. true strain curve.) Hint: Use the “Add Trendline” function in Excel to fit a power function, i.e. y = A(x^b) , to the true stress-strain curve. Figure 12: K= 414.29 N= 0.1323 d) Compare the modulus, strength, and ductility measures with published data and comment. Provide plausible explanations (or sources of error) if there are significant differences. The measurements which were gathered from the experiment and correspondingly calculated in excel were majority the same yet had slight differences. This can be due to the tightness of the clamps on the tensile test, which held the material in place. Another possible differences in measurements could be due to the placement of the material and its distance from the base of the clamp. This could cause uneven breakages or a bias towards an early or late fracture. y = 414.29x 0.1323 0 50 100 150 200 250 300 350 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 Stress Strain Power Hardening graph

11 Part II. Experimental Results and Data Analysis of Polycarbonate Samples a) Stress-strain curves 1. With the raw data obtained from the tension test, compute and plot engineering stress s vs. engineering strain e. The plot should be generated with a computer (e.g.Microsoft Excel). No credit will be given to a hand-generated plot. Figure 13: To find the engineering stress vs strain graph, one must individually calculate the Engineering Strain (stroke/original length) and Engineering Stress (force/original area) for each of the three specimens (Figure 9). Following this an average of each point must be taken in order of there to be a singular line in a singular graph (Figure 10). Engineering Strain on the X axis and Engineering Stress on the Y axis. -10 0 10 20 30 40 50 60 70 0 0.05 0.1 0.15 0.2 0.25 Eng Stress Eng Strain Similarity of Stress/Strain Curves for three Plastic tests

12 2. Compute and plot true stress s vs. true strain e. Plot on the same graph as engineering stress vs. engineering strain so that you can clearly see the differences between the curves. Figure 14: The true stress/strain curve (yellow line) was derived from the average engineering stress/strain numbers. True stress was found by multiplying engineering stress with (1+engineering strain) and true strain was found by taking ln (1 + engineering strain). b) Elastic property and strength measures 1. Determine the elastic modulus E. To determine the Modulus, we first must find the average of the 3 graphs as one graph then finding the trendline of the “straight portion” of the graph leading to the yield point. Then the slope of this line is the Elastic modulus which is y = 670.72x. 2. Determine the 0.2% offset yield strength (sY) . In order to obtain the 0.2% offset. One must first calculate the 0.2% offset yield point. To determine this one must obtain the 0.2 percent offset stress and strain. The 0.2 strain is found by adding 0.2% in excel to the average of the three strains and the stress is found through multiplying the modulus and the avg strain. The plot for this on the graph demonstrates where the yield point is (grey line and blue line). Through finding the yield point if one locates its coordinates on the graph the which is 39.45 on the y axis. y = 670.72x 0 20 40 60 80 0 0.05 0.1 0.15 0.2 Stress Strain Averages for stress vs strain for the three Plastic Tests

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13 3. Determine the ultimate tensile strength. In order to find the UTS one must locate the highest stress. This can most efficiently be completed by typing =MAX (avg stress column) into a cell. In this case the UTS is 59.54 c) Determine the failure strain of the material. In order to determine the failure strain, one must locate where the strain on the graph dips right before fracture (almost perpendicular to the x axis) after the UTS. In this case it was 0.229337773. Conclusion In conclusion the tensile testing lab brought engineering stress/strain and true stress and strain into real life and visual representation. Students were able to gain hands on experience in learning how to handle real life engineering machinery along with how the machinery interacts with our study’s. There’s an important connection when an individual is able to bridge a gap from the classroom to live experiences. This can help students not only visualize topics to a higher degree but also spark interest in leaning. The lab continued its teachings that not all materials have the same ductility or strength. Students were able to measure and observe these differences, which paved a key foundation into understanding the subject matter.